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Interfaces between oppositely charged polymers present strong local gradients in the electrical environment, enabling applications in electrochemical devices, ionic diodes, and low-voltage electroadhesives. As these responses are often highly dependent on the area of contact between the polymers, many efforts have been made to prepare structures with a high interfacial area to enhance performance. However, tailoring the miscibility of polycations and polyanions to realize targeted nanoscale structures remains an outstanding challenge. In this study, we present a novel approach to achieving microphase separation in solvent-free block polyampholytes by manipulating counterion chemistry. Using a block polyampholyte composed of a positively charged imidazolium block and a negatively charged sulfonylimide block, we demonstrate that the phase behavior can be modulated by the chemistry of the added ionic liquid salts. Specifically, immiscibility between a fixed alkyl-imidazolium and a bulky alkyl-phosphonium counterion drives microphase separation of the block polyampholyte. Theoretical predictions of microphase behavior support the experimental observation that the chemical incompatibility between like-charged species increases the propensity for microphase separation. This work highlights a facile route to realizing nanoscale structures of block polyampholytes using chemically incompatible ionic liquids. 

A non-equilibrium framework is introduced for recasting microscopic kinetic models of polymer dynamics into a compact field-theoretic form. Specifically, we adapt the Doi–Peliti formalism, which transforms a classical many-body problem into a second-quantized Schrödinger equation that is subsequently expressed as a real-time path integral using a boson coherent state basis. The framework is well-suited to the analysis of non-equilibrium, spatially inhomogeneous systems, which is illustrated using a simple Brownian dynamics model of dumbbell polymers in implicit solvent. By invoking a mean-field approximation, equations are derived that describe the coupled dynamics of polymer concentration and stress to second order in spatial gradients. New stress–concentration coupling and stress diffusion terms are found to arise from non-bonded interactions and serve to generalize previous theories beyond the dilute limit. Strategies are discussed for exploring fluctuation effects beyond the mean-field approximation, both analytically and numerically via field-theoretic simulation. The method can be extended to a wide variety of non-equilibrium polymer models, including those with reversible or irreversible chemical reactions. 

Recently, the density-explicit framework, which describes the thermodynamic properties of multicomponent polymer systems as functionals of both auxiliary and density fields, has attracted growing interest in polymer field theory simulations. This is due to the flexibility of the framework in accommodating various forms of intermolecular potentials, and in particular, the easy generalization to many-body interactions beyond pair potentials. However, numerical simulations based on the formalism are generally more expensive owing to the increased number of fields, compared to the conventional auxiliary field framework. In this work, we develop deep neural networks with efficient low-dimensional and largely local feature representations that are applicable across different spatial resolutions and dimensions to accelerate polymer field theory simulations based on this framework. Our results may serve as a stepping stone toward accurate and efficient prediction of the phase behavior of complex block copolymer mesophases, as well as a blueprint for developing machine learning-assisted field theoretic simulation tools for the computational study of polymers and soft matter systems more broadly. 

Complex fluids in confined geometries are found in numerous applications, including membranes, lubricants, and microelectronics. However, current computational approaches for studying these systems have a variety of shortcomings. Particle-based simulations are limited in accessible length and time scales, while the interaction parameters in field-theoretic approaches have no direct connections to specific chemistries. Here, we extend a multiscale framework that we earlier developed for bulk systems to address these challenges in confined polymer formulations. The methodology uses atomistic molecular dynamics simulations to parameterize coarse-grained field-theoretic models of confined fluids, which subsequently enable fast equilibration and the ability to surmount length scales inaccessible to particle-based simulation methods. We first use this workflow to study a model system consisting of a confined Gaussian fluid to validate and determine best practices for the coarse-graining methodology. Next, we demonstrate this methodology by applying it to an alkyl acrylic diblock copolymer and dodecane solution confined between α-iron oxide surfaces and examining the effect of diblock concentration and length on the structure of the adsorbed film. This approach has the potential to expedite the study of complex fluids in confined environments, bridging atomistic detail and mesoscale modeling with broad implications for materials design. 

Abstract A general algorithm is introduced to compute single‐chain partition functions in field‐theoretic simulations of polymers with nested tree‐like topologies, including self‐consistent field theory simulations that invoke the mean‐field approximation. The algorithm is an extension of a method used in a number of recent studies on the phase behavior of bottlebrush block copolymers. In those studies, the computational cost of computing single‐chain partition functions is reduced by aggregating the statistical weight of degenerate side arms. By extending this method to chains with arbitrary degrees of branching, the computational cost is reduced to scale with the total length of unique segments in the chain instead of the total length/mass of the entire chain. The method is first validated on a model dendrimer system by comparing results to coarse‐grained molecular dynamics simulations and also demonstrate its advantage over more conventional approaches to compute single‐chain partition functions. The algorithm is subsequently used to analyze the phase behavior of a molecularly informed field‐theoretic model of poly(butyl acrylate)‐graft‐poly(dodecyl acrylate) (pBA‐graft‐pDDA) copolymers in a dodecane solvent. The methodology can help advance field‐theoretic investigations of branched polymers by leveraging degeneracy in the chain to reduce computational cost and avoid the need to develop architecture‐specific algorithms.